Discovery of ultracompact dwarf galaxies in the Virgo Cluster

We have discovered nine ultracompact dwarf galaxies (UCDs) in the Virgo Cluster, extending samples of these objects outside the Fornax Cluster. Using the Two Degree Field (2dF) multifiber spectrograph on the Anglo-Australian Telescope, the new Virgo members were found among 1500 color-selected, starlike targets with 16: 0 < b(j) < 20.2 in a 2 degrees diameter field centered on M87 (NGC 4486). The newly found UCDs are comparable to the UCDs in the Fornax Cluster, with sizes less than or similar to 100 pc, -12.9 < M-B < -10.7, and exhibiting red absorption-line spectra, indicative of an older stellar population. The properties of these objects remain consistent with the tidal threshing model for the origin of UCDs from the surviving nuclei of nucleated dwarf elliptical galaxies disrupted in the cluster core but can also be explained as objects that were formed by mergers of star clusters created in galaxy interactions. The discovery that UCDs exist in Virgo shows that this galaxy type is probably a ubiquitous phenomenon in clusters of galaxies; coupled with their possible origin by tidal threshing, the UCD population is a potential indicator and probe of the formation history of a given cluster. We also describe one additional bright UCD with M-B = -12.0 in the core of the Fornax Cluster. We find no further UCDs in our Fornax Cluster Spectroscopic Survey down to bj 19.5 in two additional 2dF fields extending as far as 3 degrees from the center of the cluster. All six Fornax bright UCDs identified with 2dF lie within 0.degrees 5 (projected distance of 170 kpc) of the central elliptical galaxy NGC 1399.

The effect of local galaxy surface density on star formation for HI selected galaxies

We present the result of investigations into two theories to explain the star formation rate (SFR)-density relationship. For regions of high galaxy density, either there are fewer star-forming galaxies or galaxies capable of forming stars are present but some physical process is suppressing their star formation. We use H I Parkes All-Sky Survey's (HIPASS) HI detected galaxies and infrared and radio fluxes to investigate SFRs and efficiencies with respect to local surface density. For nearby (vel < 10 000 km s(-1)) H I galaxies, we find a strong correlation between H I mass and SFR. The number of H I galaxies decreases with increasing local surface density. For H I galaxies (1000 < vel < 6000 km s(-1)), there is no significant change in the SFR or the efficiency of star formation with respect to local surface density. We conclude that the SFR-density relation is due to a decrease in the number of H I star-forming galaxies in regions of high galaxy density and not to the suppression of star formation.

The survey for ionization in neutral gas galaxies. I. Description and initial results

We introduce the Survey for Ionization in Neutral Gas Galaxies (SINGG), a census of star formation in H I selected galaxies. The survey consists of H alpha and R-band imaging of a sample of 468 galaxies selected from the H I Parkes All Sky Survey (HIPASS). The sample spans three decades in H I mass and is free of many of the biases that affect other star-forming galaxy samples. We present the criteria for sample selection, list the entire sample, discuss our observational techniques, and describe the data reduction and calibration methods. This paper focuses on 93 SINGG targets whose observations have been fully reduced and analyzed to date. The majority of these show a single emission line galaxy (ELG). We see multiple ELGs in 13 fields, with up to four ELGs in a single field. All of the targets in this sample are detected in H alpha, indicating that dormant (non-star-forming) galaxies with M-H I greater than or similar to 3x10(7) M-circle dot are very rare. A database of the measured global properties of the ELGs is presented. The ELG sample spans 4 orders of magnitude in luminosity (H alpha and R band), and H alpha surface brightness, nearly 3 orders of magnitude in R surface brightness and nearly 2 orders of magnitude in H alpha equivalent width (EW). The surface brightness distribution of our sample is broader than that of the Sloan Digital Sky Survey (SDSS) spectroscopic sample, the EW distribution is broader than prism-selected samples, and the morphologies found include all common types of star-forming galaxies (e.g., irregular, spiral, blue compact dwarf, starbursts, merging and colliding systems, and even residual star formation in S0 and Sa spirals). Thus, SINGG presents a superior census of star formation in the local universe suitable for further studies ranging from the analysis of H II regions to determination of the local cosmic star formation rate density.

The survey for ionization in neutral gas galaxies. II. The star formation rate density of the local universe

We derive observed H alpha and R-band luminosity densities of an H I-selected sample of nearby galaxies using the SINGG sample to be l'(H alpha) = (9.4 +/- 1.8) x 10(38) h(70) ergs s(-1) Mpc(-3) for H alpha and l'(R) = (4.4 +/- 9.7) x 10(37) h(70) ergs s(-1) angstrom(-1) Mpc(-3) in the R band. This R-band luminosity density is approximately 70% of that found by the Sloan Digital Sky Survey. This leads to a local star formation rate density of log ((rho)over dot(SFR) [M-circle dot yr(-1) Mpc(-3)]) = -1.80(-0.07)(+0.13)(random) +/- 0.03(systematic) + log (h(70)) after applying a mean internal extinction correction of 0.82 mag. The gas cycling time of this sample is found to be t(gas) = 7.5(-2.1)(+1.3) Gyr, and the volume-averaged equivalent width of the SINGG galaxies is EW(H alpha) = 28.8(-4.7)(+7.2) angstrom (21.2-3.5+4.2 angstrom without internal dust correction). As with similar surveys, these results imply that (rho)over dot(SFR)(z) decreases drastically from z similar to 1.5 to the present. A comparison of the dynamical masses of the SINGG galaxies evaluated at their optical limits with their stellar and H I masses shows significant evidence of downsizing: the most massive galaxies have a larger fraction of their mass locked up in stars compared with H I, while the opposite is true for less massive galaxies. We show that the application of the Kennicutt star formation law to a galaxy having the median orbital time at the optical limit of this sample results in a star formation rate decay with cosmic time similar to that given by the. (rho)over dot(SFR)(z) evolution. This implies that the (rho)over dot(SFR)(z) evolution is primarily due to the secular evolution of galaxies, rather than interactions or mergers. This is consistent with the morphologies predominantly seen in the SINGG sample.

A variational method and approximations of a Cauchy problem for elliptic equations

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.

An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

An iterative procedure for solving a Cauchy problem for second order elliptic equations

An iterative method for reconstruction of solutions to second order elliptic equations by Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the elliptic operator and its adjoint. The convergence proof of this method in a weighted L2 space is included. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

On a Class of Generalized Elliptic-type Integrals

The aim of this paper is to study a generalized form of elliptic-type integrals which unify and extend various families of elliptic-type integrals studied recently by several authors. In a recent communication [1] we have obtained recurrence relations and asymptotic formula for this generalized elliptic-type integral. Here we shall obtain some more results which are single and multiple integral formulae, differentiation formula, fractional integral and approximations for this class of generalized elliptic-type integrals.

Key Agreement Protocol Using Elliptic Curve Matrix Power Function

* Work is partially supported by the Lithuanian State Science and Studies Foundation.

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30

Estimate for the Number of Zeros of Abelian Integrals on Elliptic Curves

2000 Mathematics Subject Classification: Primary 34C07, secondary 34C08.

Complete Integrability of a Nonlinear Elliptic System, Generating Bi-umbilical Foliated Semi-symmetric Hypersurfaces in R^4

Николай Кутев, Величка Милушева - Намираме експлицитно всичките би-омбилични фолирани полусиметрични повърхнини в четиримерното евклидово пространство R^4

Lp Microlocal Properties for Multi-Quasi-Elliptic Pseudodifferential Operators

2010 Mathematics Subject Classification: Primary 35S05; Secondary 35A17.

On the Holomorphic Extension of Solutions of Elliptic Pseudodifferential Equations

2010 Mathematics Subject Classification: 35B65, 35S05, 35A20.